Derivative-Free & Order-Robust Optimisation

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose VROOM, a zeroth order optimisation algorithm capable of achieving vanishing regret in non-stationary environments, while recovering favorable rates under stochastic reward-generating processes. Our results are the first to target simple regret definitions in adversarial scenarios unveiling a challenge that has been rarely considered in prior work.